Error-Savvy Analysis and Design of Batch Partitioning Measurements

Probabilistic modeling of the transport of ground-water constituents requires accurate characterization of the partitioning of these constituents between aqueous and immobile phases. The most common method of estimating partitioning is the batch sorption test, which is used to measure Kd values (solid-water partitioning) and Koc values (organic carbon-water partitioning). Although procedures for these tests are provided by various government agencies (e.g., ASTM D 4646 and EPA402-R-99-004A), the sources do not explain how to optimize the tests to constrain uncertainty nor the importance of doing so. Consequently, the uncertainty of a set of partitioning measurements can be extreme and even absurd. Such data sets, which are commonplace, hamper probabilistic modeling efforts. Monte Carlo simulations were conducted to demonstrate how the propagation of analytical uncertainty from standard ASTM D 4646 batch tests can cause partitioning (Kd) uncertainty that is both unnecessarily large and awkwardly skewed. An alternate error-savvy design requires an initial suite of tests where the ratio of solid to water is varied to identify the solid-water ratio that causes approximately half of the constituent to partition to the solid phase. Setting subsequent principal sets of batch experiments to this ratio allows simple statistical characterization of the partitioning behavior because the log of these measurements will be approximately linearly related to the fraction partitioned. If instead a large portion of the measurements falls outside of this linear range (i.e., percentage sorbed below 20 percent or above 80 percent) due to a solid-water ratio that is too low or too high, then the partitioning distributions become highly skewed and unwieldy. In addition, the analytical uncertainties can result in 1) detection limit problems, 2) decreased precision and accuracy at low concentrations, 3) large uncertainty in the fraction immobilized, or 4) aqueous measurements that exceed the initial concentrations. The first two conditions occur when there is too much partitioning to the solid phase, and the latter two occur when there is too little. Additionally, the fourth condition results in negative partitioning values, which are illogical and commonly discarded. Some of these issues can be partially or fully resolved after the fact, but some cannot. The Monte Carlo simulations demonstrate that the error-savvy design advocated here minimizes uncertainty in partitioning measurements and allows improved probabilistic characterization for transport modeling. This approach may not be feasible in every situation, however, and should not preclude the use of other methods of measuring mobility, such as column experiments and in situ partitioning measurements.